C. when the center of earth is 2 × 108 kilometers from the center of mars, the force of gravity between the two planets is about 64.32 × 1022 newtons. the mass of earth is about 6 × 1024 kilograms, and the mass of mars is about 6.4 × 1023 kilograms. using these values, estimate the gravitational constant.

The equation for gravitational attractive force is: F = G(m1)(m2)/r^2. For this case, we have F = 64.32 x 10^22 N, m1 = 6 x 10^24 kg, m2 = 6.4 x 10^23 kg, and r = 2 x 10^8 km = 2 x 10^11 m.
Substituting:
64.32 x 10^22 N = (G)(6 x 10^24 kg)(6.4 x 10^23 kg)/(2 x 10^11 m)^2
G = 6.7 x 10^-3 m^3/kg-s^2
This value is far from the expected 6.67 x 10^-11 m^3/kg-s^2, though it may be because the value for the force of gravity is quite far from the usual values in literature nowadays.